Question 550155
Let {{{ x }}} = the original length in meters
{{{ 200/x }}} = original cost/meter
{{{ 200 / x - 2 }}} = the new cost/meter
{{{ ( x + 5 )*( 200/x - 2 ) = 200 }}} us
{{{ 200 + 1000/x - 2x - 10 = 200 }}}
Subtract {{{200}}} from both sides
{{{ 1000/x = 2x + 10 }}}
Multiply both sides by {{{x}}}
{{{ 1000 = 2x^2 + 10x }}}
{{{ x^2 + 5x - 500 = 0 }}}
Use the quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{ a = 1 }}}
{{{ b = 5 }}}
{{{ c = -500 }}}
{{{ x = (-5 +- sqrt( 5^2-4*1*(-500) ))/(2*1) }}} 
{{{ x = (-5 +- sqrt( 25 + 2000 )) / 2 }}} 
{{{ x = (-5 +- sqrt( 2025 )) / 2 }}} 
{{{ x = (-5 + 45) / 2 }}} ( can't use the (-) square root )
{{{ x = 20 }}}
The piece is 20 m long
{{{ 200/x = 200/20 }}}
{{{ 200/x = 10 }}}
The original price/m is 10 us
check answers:
{{{ ( x + 5 )*( 200/x - 2 ) = 200 }}}
{{{ ( 20 + 5 )*( 200/20 - 2 ) = 200 }}} 
{{{ 25*( 10 - 2 ) = 200 }}}
{{{ 25*8 = 200 }}}
{{{ 200 = 200 }}}
OK